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arXiv · 1510.07860

Tongues in Degree 4 Blaschke Products

Jordi Canela·Núria Fagella·Antonio Garijo
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Abstract

The goal of this paper is to investigate the family of Blasche products $B_a(z)=z^3\frac{z-a}{1-\bar{a}z}$, which is a rational family of perturbations of the doubling map. We focus on the tongue-like sets which appear in its parameter plane. We first study their basic topological properties and afterwords we investigate how bifurcations take place in a neighborhood of their tips. Finally we see how the period one tongue extends beyond its natural domain of definition.

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Jordi Canela, Núria Fagella, Antonio Garijo. 2015-10-27. Tongues in Degree 4 Blaschke Products. https://doi.org/10.1088/0951-7715%2F29%2F11%2F3464

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